Zaman gecikmeli sistemler için kural kaydırma tabanlı bulanık mantık kontrolör tasarımı

Abstract

Zaman gecikmeli sistemlerin kontrolü pratikte en çok karşılaşılan kontrol problemlerinden biridir. Literatürde bu kontrol problemi üzerine pek çok çalışma ve uygulama bulunmaktadır. Zaman gecikmeli sistemlerde karşılaşılan sorunların temeli sistemden gözlenen bilginin geçmişe ait olmasına dayanmaktadır. Bu durumun kontrolör tarafından algılanması mümkün olmadığı için başarısız sonuçlara neden olabilmektedir. Probleme temel bir bakış açısıyla yaklaşmak gerekirse, kontrol sistemine giren bilginin geçmiş zamana ait olması durumunda bunun algılanıp duruma göre bir ayarlama yapılmasının soruna çözüm olması beklenir. Bulanık mantık kontrol yapıları üzerine yapılan çalışmalardan bazıları kontrolörün katsayılarını değiştirmeden kural tabanının kaydırılması ile zaman gecikmesinin sistem yanıtı üzerindeki olumsuz etkilerinin azaltılabileceğini göstermiştir. Sistem modelleri elde edilirken sahip olabilecekleri zaman gecikmesinin dikkate alınmış olması gerekir. Ancak zaman gecikmesinin gerçekte modelde bulunan değerinden farklı olduğu durumlar ile karşılaşılabilir. Bu durumda kontrol sisteminden beklenilen başarım elde edilemez. Bu çalışmada, ölü zamanın modelde bulunan değerinden daha az veya daha fazla olduğu durumlar için modele göre belirlenmiş bulanık mantık PID kontrolörünün kural tablosu değiştirilmiştir. Bu işlem sırasında bulanık kontrolör kural tablosu satırları uygun miktar ve yönlerde kaydırılmıştır. Kural tablosunun düzenlenmesinin etkisini görebilmek adına çalışmalar boyunca her bir sistem modeli için bulanık mantık kontrol katsayıları genetik arama algoritması yardımıyla belirlenmiştir. Genetik arama algoritması için arama kriteri zaman ağırlıklı hata karelerinin toplamı (ITSE) olarak seçilmiştir. ITSE kriteri aynı zamanda sistemin farklı kural tabanları ile başarımını incelemek için de kullanılmıştır. Ayrıca, sistemdeki zaman gecikmesinin değişmesi durumuna kontrol yönteminin bu değişime bağlı olarak uygun kural tabanını kullanabilmesi için öz-ayarlamalı kural tabanı yöntemi önerilmiştir. Bu amaçla sistem modelinde var olan zaman gecikmesinin çeşitli değişimleri için uygun olan kural tabanları belirlenmiştir. Bu kural tabanları arasında, belirlenen zaman gecilmesine bağlı olarak geçiş yapabilen bir kontrol yapısı kurulmuştur. Öz ayarlamalı kontrol yapısı, kural tabanı kaydırılmamış bulanık mantık kontrol yöntemi ve zaman gecikmesi bilinen sistemler için belirlenmiş olan kural tabanı kaydırılmış bulanık mantık kontrol yöntemi ile karşılaştırılmıştır. Elde edilen ITSE değerleri tablolar halinde verilirken, sistem yanıtları grafik halinde gösterilmiştir. Tahmin edilebileceği gibi zaman gecikmesi bilinen sistemler için uygun kural tabanı kaydırması ile elde edilen kontrol sistemlerinin benzetim sonuçları öz-ayarlamalı kontrol yönteminin uygulandığı zaman gecikmesi bilinmeyen sistemlerin benzetim sonuçlarından belirlenen başarım kriterine göre daha başarılı olmuştur. Fakat, çizelge ve grafikler göstermektedir ki öz-ayarlamalı kontrol yöntemi ile kural tabanı kaydırılmamış bulanık mantık kontrol yöntemini kıyaslandığında öz-ayarlamalı kural tabanı yapısı daha başarılı olmuştur.

Time delay, which can be roughly defined as the effects of a signal given at the input of a system, to be observed with a certain time difference at the output of the system, is an unavoidable physical phenomenon for many physical systems. Although this phenomenon can occur for many reasons, the time delay in a control system is usually due to the internal nature of the system itself, controller-related reasons, and/or sensors. Time delay in a control system has undeniable effects on the system, especially as its amount increases. The control of systems with time delay is one of the most common control problems in practice. There are many studies and applications of this control problem in the literature. In this thesis, the effect of time delay on fuzzy control systems is handled. Fuzzy Logic is a mathematical discipline that we use in our daily life and that brings our behavior to the structure we interpret. We see the concepts of Fuzzy Logic in many parts of our lives. These concepts are high, medium, and low values. Besides; includes very low, medium, and very high intermediate values. The fuzzy set is the basis of Fuzzy Logic. Fuzzy sets are the most basic elements of fuzzy systems. The first explanation of fuzzy sets was put forward in 1965 by Prof. Dr. Lotfi A. Zadeh. In the classical set approach, the elements either belong to that set (1) or do not (0). However, in the Fuzzy Logic approach, the belonging of the elements to that set varies between 0 and 1. As a first application, the speed and performance of a steam turbine were very successfully controlled with a Fuzzy Logic based system. Nowadays, fuzzy logic control is successfully used in the control of many types of linear, nonlinear, and time-delayed systems. As it has been already explained the basis of the problems encountered in systems with time delay is based on the fact that the information observed from the system belongs to the past. Since it is not possible for the controller to detect this situation, a successful performance cannot be obtained from the output of the control system, especially in cases where the time delay is large. When the problem is approached from a fundamental point of view, if the information fed into the control system belongs to a time earlier than that moment, it should be detected and adjusted accordingly. In literature, there are various studies on the control of systems with time delay. Previously, a study on fuzzy logic control has shown that successful performances can be obtained on the control of systems with time delay by only shifting the rule base in a proper way without changing the coefficients of the controller. In that study, symmetrical rule bases used for systems without time delay are considered and it is focused on how the table should be shifted if there is a dead time in the same system. During this process, a special performance criterion that depends on a desired time-domain criteria has been tried to be made optimal. Therefore, the rule base shifting is always in the same direction. In this thesis, we deal with the systems modeled with a certain time delay. However, the time delay of the system may differ from the value considered for its system model. It is possible for this time delay to be different from its value in the system model or change in time in the positive direction as well as in the negative direction. In this study, it is first shown that it is possible to regulate the fuzzy rule base of the controller not only for the increase but also for the decrease of the time delay. The system error and the derivative of the system error at the fuzzy logic input and the control signals at the fuzzy logic output are to be scaled for integration between the rule base and the system. In order to see the effect of the regulation of the rule base, the fuzzy logic control coefficients found by the genetic algorithm for each system were kept constant throughout the studies. These scaling coefficients can be calculated using many different methods. In general, these calculations are made by optimizing an objective function using a global search algorithm. The objective function (cost function) is critical for the correct orientation of the optimization algorithms. In this regard, there are many common cost functions such as integral time absolute error (ITAE), integral square error (ISE), integral time square error (ITSE), and integral absolute error (IAE). The integral time square error (ITSE) is selected as the cost function in this study. After determining the cost function, an algorithm is determined to solve this optimization problem. For this purpose, there are lots of optimization algorithms such as big-bang big-crunch algorithm, genetic algorithm, stochastic gradient descent, min-batch gradient descent, and gradient descent with momentum. The genetic algorithm is one of the most popular and it is used for minimizing the cost function in this study. And finally, the boundary conditions in which the algorithm can scan are determined. To sum up, the integral time square error (ITSE) value of the system is used as the objective function to be minimized by the genetic algorithm. At the same time, ITSE values are compared to examine the performance of the system with different rule bases. In addition to all these, it is a predictable fact that delay time in systems can change with time. It is also obvious that it is not always possible to intervene in the case of changing the time delay. A control method that can update itself considering the change in time delay would be very useful. For this purpose, a self-adjusting rule base method is proposed so that the control method can use the appropriate rule base depending on the change in time delay. While examining the rule base regulations, at the same time, the rule bases suitable for the system were determined depending on corresponding time delays. While working on the rule bases recommended for the increase and decrease of the time delay in the system, the rule bases that give the best performance value for different time delays of the system were determined. An online control structure that can switch between these determined rule bases depending on the time delay has been established. This control structure is compared with the rule base shifted fuzzy logic control method and the rule base shifted fuzzy logic control method for systems with known time delay. The ITSE values obtained are given in tables and the system responses are shown in graphs. As it is expected, the performances of the control systems obtained with the appropriate rule base shift for the systems with known time delay were more successful than the performances of the systems with unknown dead time in which the self-adjusted control method was applied. However, the tables and graphs clearly show that the self-adjusted rule base structure is more successful when compared with the fuzzy logic control method which has non-shifted rule base. In summary, for systems with known time delay it is recommended to work with an appropriately shifted rule table, and for systems with unknown or variant time delay it is recommended to use the self-adjusting rule base method. Two conclusions are reached in this study. The first is that in a fuzzy logic control system if the time delay changes, the system can be successfully controlled by simply updating the rule base. The change of the time delay mentioned here includes both the increase and decrease of the time delay and therefore, the rule base is shifted to both sides accordingly. The second conclusion is that in case the time delay changes the self-adjusted rule base supports the fuzzy control system to continue its good performance.